Sheep and cows eat grass (non-fat) and walk all day (excercise).
Why do we get so much fatty meat?

Aladin Bekhit, a food scientist at the University of Otago, responded.

Grasses contain very small amounts of fat (about 2-4% on dry weight basis,
that is the weight after removing the water from the grass). Most of the fat is
formed from the carbohydrates present in the feed (their content will vary
depending on the grass type and form). Several biochemical pathways are
involved that convert carbohydrates into fatty acids (the building blocks
of fat) that occur in liver, the tissue that stores the fat "called adipose tissue",
and the mammary gland.

Most of the carbohydrates are used for energy production and the excess
amount of carbohydrates is stored in a form that can be easily metabolized
when energy is needed.

In animals the stored carbohydrates is of glycogen. However, carbohydrates
are solvated by water and large amounts of carbohydrates cannot be
stored in the form of glycogen. Nature evolved a better way to store the
energy reserves in the form of fat deposited in various parts of the animal body.

The conversion of the carbohydrates to fat is carried out through several
biochemical reactions that starts with the conversion to pyruvate, then to
acetyl Coenzyme A, followed by carboxylation reaction, by an enzyme
called acetyl Coenzyme A carboxylase, that generate malonyl Coenzyme A.
The latter compound is the substrate used for the fatty acid biosynthesis.

The deposited fat is distributed at molecular level (such as the cell membrane),
inside muscles (known as marbling in meat cuts), between muscles or as
a layer around the meat (known as adipose fat). The fat content and the
degree of fat saturation (classified based on the contents of saturated,
mono- and unsaturated fatty acids content) contribute to the appearance,
flavour and the shelf life of meat and meat products. Therefore, they play
important roles in the consumers' acceptability of meat products.